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" PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given triangle : it is required to inscribe a circle in the triangle ABC. "
Elements of Geometry: With, Practical Applications - Σελίδα 147
των George Roberts Perkins - 1850 - 320 σελίδες
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The new practical gager

Matthew Iley - 1820
...at right angles. Then join AB, BD, DC, and CA ; the figure ABCD is the square required. PROBLEM III. To inscribe a circle in a given triangle. Let ABC be the triangle in which ii is required to inscribe a circle. About the angular points B and C, with any convenient...

Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 σελίδες
...triangle equiangular to the triangle DEF. Therefore about a given circle, &c. QEF I PROPOSITION IV. PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given triangle; it is required to inscribe a circle in the triangle ABC. Bisect the angles ABC, AC в, by the right...

Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - 1828 - 316 σελίδες
...CB=CD ; hence they are equal ; hence AD is equal to AB, and also the angle CAD to CAB. PROBLEM. 1 53. To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B, by the lines AO and BO, meeting in the point O ; from the point O, let fall the perpendiculars...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1836 - 359 σελίδες
...bisects the angle formed by two tangents, must pass through the centre .of the circle. PROBLEM XV. To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B, by the lines AO and BO, meeting in the point O ; from the point O, let fall the perpendiculars...

Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845
...segment would be a semicircle; and consequently the centre would be the middle of AB. PROBLEM XVIII. To inscribe a circle in a given triangle. • Let ABC be the given triangle. Bisect the angles A and B, by the lines AO and BO, meeting in the point O ; from the point O, let fall the perpendiculars...

Elements of Drawing and Mensuration Applied to the Mechanic Arts: A Book for ...

Charles Davies - 1846 - 240 σελίδες
...point of intersection, draw the lines AD and CD, and ABCD will be the required rhombus. 42. How do you inscribe a circle in a given triangle? Let ABC be the given triangle. Bisect either two of the angles, as A and C, by the lines AO and CO, and the point of intersection O will...

The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...equiangular to the given triangle DEF, and it is described about the given circle ABC. QEF PROP. IV. PBOB. To inscribe a circle in a given triangle. Let ABC be the given triangle : it is required to inscribe a circle in the triangle ABC. Bisect the angles ABC, ACB by the straight...

Elements of Geometry: With Practical Applications ...

George Roberts Perkins - 1847 - 308 σελίδες
...the two triangles AFG, AFH, we see that the angles AGF and AHF are equal, each being a right angle ; also the angles FAG, FAH are equal, since AF bisects...and consequently be the inscribed circle required. Cor. The three lines bisecting the three angles of a triangle meet at the same point, which point is...

Principles of geometry, mensuration, trigonometry, land-surveying, and ...

Thomas Tate (mathematical master.) - 1848
...Cor. 3. Regular polygons are not only equilateral, but also equiangular ; thus, /ABC=Z.BCD — &c. 69. PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given triangle; bisect A the angles BCA and CBA (Art. 21.) by the lines CD and BD meeting each other in the point D; from...

Mensuration, Mechanical Powers and Machinery: The Principles of Mensuration ...

Daniel Adams - 1849 - 128 σελίδες
...and the radius DE, describe a circle, and it will be inscribed in the given polygon. PROBLEM XXXIII. To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect any two angles, as A and B, and the point D, where the bisecting lines cross each other, will be the...




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